Systems of Inequalities

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables. The solution is the region where the graphs of the inequalities overlap.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a dashed or solid line, depending on whether the inequality is strict (<, >) or inclusive (≤, ≥). Then, shade the appropriate region based on the inequality.

Front

What does it mean to shade above or below a line in a graph?

Back

Shading above a line indicates that the solutions to the inequality are greater than the line (y > mx + b), while shading below indicates that the solutions are less than the line (y < mx + b).

Front

What is the significance of the inequality symbol in graphing?

Back

The inequality symbol determines whether the line is dashed (for < or >) or solid (for ≤ or ≥) and indicates which side of the line to shade.

Front

What does it mean if a system of inequalities has no solution?

Back

A system of inequalities has no solution if the shaded regions of the inequalities do not overlap, meaning there are no points that satisfy all inequalities simultaneously.

Front

What does it mean if a system of inequalities has infinite solutions?

Back

A system of inequalities has infinite solutions if the shaded regions overlap completely, meaning there are infinitely many points that satisfy all inequalities.

Front

How do you determine the solution set for a system of inequalities?

Back

The solution set for a system of inequalities is determined by finding the region where the shaded areas of all inequalities intersect.

Front

What is the difference between a strict and non-strict inequality?

Back

A strict inequality (< or >) does not include the boundary line, while a non-strict inequality (≤ or ≥) includes the boundary line.

Front

Back

Front

How do you solve a system of inequalities graphically?

Back

To solve a system of inequalities graphically, graph each inequality on the same coordinate plane and identify the overlapping shaded region.